U.S. private-equity giant Carlyle Group LP is nearing a deal to buy Tyco International Ltd.'s South Korean home security unit, according to people familiar with the matter.

The sale to Carlyle of the business, known as Caps, could be announced this week and is likely to carry a price tag of $1.5 billion or more, some of the people said. There is still the possibility it will fall apart at the last minute. Assuming it doesn't, Carlyle...